Elementary School Math Quiz: Solve Unit Fraction Division Problems

Maria has $\frac{1}{3}$ of a pizza that she wants to share equally among 4 people. After sharing the pizza, she realizes she needs to buy 2 more whole pizzas to feed everyone properly. How much pizza will each person get from Maria's original $\frac{1}{3}$ pizza?

A coach has 2 gallons of sports drink. Each player gets $\tfrac{1}{4}$ gallon. This is $2 \div \tfrac{1}{4}$, which answers "how many $\tfrac{1}{4}$-gallon servings are in 2 gallons." How many players can get a full serving?

Model: Think of 2 whole gallons. Each gallon can be split into 4 fourths; count the total fourths.

A gardening club has 5 meters of rope. They cut it into pieces that are each $\tfrac{1}{5}$ meter long.

You can model this by drawing 5 whole-meter bars, and splitting each bar into 5 equal parts. This division answers "how many $\tfrac{1}{5}$-meter groups are in 5 meters."

What is the correct answer to $5 \div \tfrac{1}{5}$?

A recipe uses $\tfrac{1}{2}$ cup of yogurt. You have 4 friends, and you want to share the yogurt equally so each friend gets the same amount. This division answers "how much in each group." What is $\tfrac{1}{2} \div 4$ and what does it mean in this situation? (Model: Picture $\tfrac{1}{2}$ cup as 1 bar cut into 2 equal parts, then split that amount into 4 equal shares.)

A baker has 4 whole pies. Each slice is $\tfrac{1}{8}$ of a pie. This division answers "how many slices of size $\tfrac{1}{8}$ are in 4 pies." What is $4 \div \tfrac{1}{8}$? (Model: Draw 4 circles and divide each circle into 8 equal slices.)

A baker has $\tfrac{1}{3}$ kilogram of dough. She divides it equally among 2 trays. This division answers "how much dough is in each tray when $\tfrac{1}{3}$ kilogram is shared into 2 equal groups." Imagine a rectangle representing $\tfrac{1}{3}$ kg split into 2 equal parts.

Which explanation matches the situation?

A 3-foot board is cut into pieces that are each $\tfrac{1}{3}$ foot long.

You can model this by drawing 3 one-foot segments, and splitting each foot into 3 equal parts. This division answers "how many $\tfrac{1}{3}$-foot pieces are in 3 feet."

What is the correct answer to $3 \div \tfrac{1}{3}$?

A pitcher has $\tfrac{1}{3}$ gallon of lemonade. The coach pours it equally into 4 cups.

Think of the $\tfrac{1}{3}$ gallon as one whole divided into 3 equal parts, and then share that one part among 4 equal groups. This division answers "how much lemonade is in each cup."

Which value matches $\tfrac{1}{3} \div 4$?

A science club has $\tfrac{1}{4}$ liter of colored water. They pour it equally into 5 tiny cups. This division answers "how much is in each cup when $\tfrac{1}{4}$ liter is shared into 5 equal groups."

Which value matches $\tfrac{1}{4} \div 5$?

A water bottle holds 2 liters. A camper pours water into cups that each hold $\tfrac{1}{8}$ liter.

Imagine a number line from 0 to 2 liters marked in steps of $\tfrac{1}{8}$ liter. This division answers "how many $\tfrac{1}{8}$-liter cups fit into 2 liters."

What is the correct answer to $2 \div \tfrac{1}{8}$?

A craft club has 2 yards of ribbon. Each bookmark needs $\tfrac{1}{4}$ yard of ribbon. This division answers "how many groups of $\tfrac{1}{4}$ are in 2." What is $2 \div \tfrac{1}{4}$ and what does it tell you? (Model: Draw 2 long strips and cut each strip into fourths.)

A teacher has $\tfrac{1}{2}$ of a pan of brownies left. She shares it equally among 3 students. Think of the $\tfrac{1}{2}$ pan as a bar split into 2 equal parts, then divide that half into 3 equal groups. This division answers "how much brownie is in each group."

What is the correct answer to $\tfrac{1}{2} \div 3$?

A craft club has $\tfrac{1}{4}$ yard of string. They want to share it equally among 2 students. This is $\tfrac{1}{4} \div 2$, which answers "how much string is in each group" (each student). How much string does each student get?

Model: Imagine 1 yard split into 4 equal parts. Take 1 part, then split that part into 2 equal pieces.

A 5th grader has 4 cups of birdseed. Each feeder needs $\tfrac{1}{2}$ cup. This is $4 \div \tfrac{1}{2}$, which answers "how many $\tfrac{1}{2}$-cup groups are in 4 cups." How many feeders can be filled?

Model: Draw 4 cups on a number line from 0 to 4 and mark off halves; count the half-cup jumps.

A ribbon is $\tfrac{1}{3}$ yard long. It is cut into 2 equal pieces. This division answers "how much ribbon is in each group when $\tfrac{1}{3}$ yard is shared equally by 2."

What is the correct answer to $\tfrac{1}{3} \div 2$?

Error check: Malik says, "$1 \div \tfrac{1}{5} = \tfrac{1}{5}$ because dividing always makes the number smaller." The situation is: 1 meter of string is cut into pieces that are each $\tfrac{1}{5}$ meter. Division here answers "how many $\tfrac{1}{5}$-meter pieces are in 1 meter." Which claim about this division is incorrect?

A recipe uses $\tfrac{1}{2}$ cup of yogurt. You want to split that yogurt equally into 4 mini cups for a tasting station. This is $\tfrac{1}{2} \div 4$, which answers "how much yogurt is in each group" (each mini cup). What is the correct amount of yogurt in each mini cup?

Model: Imagine 1 cup split into 2 halves. Take 1 half, then split that half into 4 equal parts.

A recipe uses $\tfrac{1}{3}$ cup of oil. You only have a $\tfrac{1}{12}$-cup measuring spoon. This division answers "how many $\tfrac{1}{12}$-cup scoops make $\tfrac{1}{3}$ cup." Imagine a measuring-cup model where $\tfrac{1}{3}$ is marked on a cup and the cup is partitioned into twelfths.

What is the correct answer to the problem?

A teacher has $\tfrac{1}{4}$ of a yard of ribbon. She cuts it into 2 equal pieces. This division answers "how much ribbon is in each group when $\tfrac{1}{4}$ is shared into 2 equal groups." Imagine an area model: a rectangle representing $\tfrac{1}{4}$ yard split into 2 equal parts.

What is the correct answer to the problem?

A hiker has 3 miles left to walk. Each rest break happens every $\tfrac{1}{2}$ mile. This division answers "how many $\tfrac{1}{2}$-mile groups are in 3 miles." What is $3 \div \tfrac{1}{2}$ and what does it represent?